A comparison of two methods of calculating wing loading with allowance for compressibility with appendix: note on Falkner's method for calculating compressibility effects on wing loading

Abstract

The report gives the results of a comparison by two different methods of the aerodynamic loading of a tapered V wing of aspect ratio 5.8 and 45 deg sweepback at M = 0.8, based on the Prandtl-Glauert factor or linear perturbation theory; the first method, associated particularly with vortex-lattice theory, deals with changes in Mach number by preserving the plan of the wing and using special Tables of downwash, while the second uses the solution for Mach number 0 on a wing with the lateral dimensions reduced by a specified factor. The two methods are shown to be in good general agreement at M = 0.8 and, although it can be argued that the second method is more accurate on theoretical grounds, this is offset by the fact that the first has considerable advantages in ease of calculation, and in the possibility of extension to more accurate solutions when the Prandtl-Glauert factor fails at high subsonic speeds. Examples of the application of the theory are also given for a delta wing, for a straight tapered wing without sweep, and for a tapered wing with 28-4 deg sweepback. It is possible to give a general and reasonable explanation of the nature of the variations of load grading and local aerodynamic centre which occur with increasing Mach number, and with the information given, there should be no difficulty in the prediction of Mach number effects on a wide range of plan forms. Since the completion of the work, a mathematical examination of the limitations of the first method has been made by W. P. Jones who has calculated exact values of downwash due to a rectangular vortex over a range of Mach numbers for comparison with those obtained by the approximate formula. His work, which is included as an Appendix, confirms the accuracy of the approximate method at high Mach numbers.